Question

Please consider the following data set. The initial row provides labels for two variables (i.e., X1 and X2). Each subsequent row represents a pair of related scores from the same person at two different points in time.

X1 X2
2 4
6 7
7 6
3 5
8 9
Compute the appropriate t statistic to test the null hypothesis that there is no difference between means. When computing the t statistic, please retain a minimum of four decimal places for all intermediate steps (when relevant). For your final answer, please report the absolute magnitude of the t statistic with a minimum of three decimal places.

Answer 1

There is no significant difference between the means.

Explanation:

Given is the data set for X1 and x2 are we have to do a paired t test.

`H_0: \bar X_1 = \bar X_2\\H_a: \bar X_1 \\eq \bar X_2`

(Two tailed test at 5% significance level)

Mean difference = 1.00

Std error for difference = 1.225

df=4

Test statistic = mean diff/se = 1.826

p value =0.142

Since p >0.05 our alpha we accept H0

There is no significant difference before and after averages at 5% sign. level.